Providing universal health care would require the government to oversee the operation of all health care facilities and workers; essentially the entire medical establishment would go on the federal payroll. This would be a huge undertaking, but has the advantage of potentially equalizing access to good (or at least uniform) care for everyone.
To provide universal health insurance is slightly different. In this scenario the medical establishment would continue to finction as it does now, but would bill a single federal agency to get paid. One advantage to this from an administrative standpoint is that we alreay have a system in place -Medicaid and Medicare - which works this way; simply expanding that to cover everyone is somewhat less complex than setting up universal care.